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Wikipedia

In mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas. Atoms are thus the simplest well-formed formulas of the logic. Compound formulas are formed by combining the atomic formulas using the logical connectives.

The precise form of atomic formulas depends on the logic under consideration; for propositional logic, for example, the atomic formulas are the propositional variables. For predicate logic, the atoms are predicate symbols together with their arguments, each argument being a term. More precisely, the well-formed terms and propositions of ordinary first-order logic have the following syntax:

(terms)	t	::=	x > f (t₁, …, t_n)
(propositions)	A, B, …	::=	P (t₁, …, t_n) > A ∧ B \| ⊤ \| A ∨ B \| ⊥ \| A ⊃ B \| ∀x. A \| ∃x. A

The formulae of the form P (t₁, …, t_n) are the atomic formulas. Any well-formed formula—for example, ∀x. P (x) ∧ ∃y. Q (y, f (x)) ∨ ∃z. R (z)— comprises the atoms